Well this is what I did.
x^2 + y^2 = R^2 \\ y=R-\frac{1}{2}gt^2, x = v_it \\ $Subbing them in, v_i^2t^2 + R^2 - Rgt^2 + \frac{1}{4}g^2t^4=R^2 \\ v_i^2 - Rg + \frac{1}{4}g^2t^2 = 0 \\ v_i^2 = Rg - \frac{1}{4}g^2t^2 \\ $At $ t =0, v_i^2 = Rg,
\therefore $ minimum value for $ v_i $ is $ v_i =...